Localized Components Analysis

Abstract. We introduce Localized Components Analysis (LoCA) for describing surface shape variation in an ensemble of biomedical objects using a linear subspace of spatially localized shape components. In contrast to earlier methods, LoCA optimizes explicit

LocalizedComponentsAnalysis

DanAlcantara1,a,OwenCarmichael1,a,b,EricDelson2,3,

WillHarcourt-Smith2,3,KirstenSterner3,StephenFrost4,RebeccaDutton5,PaulThompson5,HowardAizenstein6,a,OscarLopez6,b,JamesBecker6,a,b,c,

andNinaAmenta1,a

ComputerScienceandbNeurologyDepartments,UniversityofCalifornia,Davis

2LehmanCollegeoftheCityUniversityofNewYork

3NYCEP,AmericanMuseumofNaturalHistory

4AnthropologyDepartment,UniversityofOregon

5NeurologyDepartmentandLaboratoryofNeuroImaging,UniversityofCalifornia,

LosAngeles

6abcPsychiatry,Neurology,andPsychologyDepartments,UniversityofPittsburgh1a

Abstract.WeintroduceLocalizedComponentsAnalysis(LoCA)fordescribingsurfaceshapevariationinanensembleofbiomedicalob-jectsusingalinearsubspaceofspatiallylocalizedshapecomponents.Incontrasttoearliermethods,LoCAoptimizesexplicitlyforlocalizedcomponentsandallowsa exibletrade-o betweenlocalizedandconciserepresentations.ExperimentscomparingLoCAtoavarietyofcompetingshaperepresentationmethodson2Dand3DshapeensemblesestablishthesuperiorabilityofLoCAtomodulatethelocality-concisenesstrade-o andgenerateshapecomponentscorrespondingtointuitivemodesofshapevariation.Ourformulationoflocalityintermsofcompatibilitybetweenpairsofsurfacepointsisshowntobe exibleenoughtoen-ablespatially-localizedshapedescriptionswithattractivehigher-orderpropertiessuchasspatialsymmetry.

1Introduction

Theparameterizationofanensembleofbiomedicalshapesisakeystepinabroadarrayofscienti candmedicalapplicationsthatrequirequanti cationoftheshapepropertiesofphysicalobjects.Inthispaper,shapeparameterizationreferstotheproblemofconvertingarepresentationofthedelineatingbound-aryofanobjectin2Dor3Dintoaconcisevectorofnumbersthatcapturesitssalientshapecharacteristics.Convertingthepotentiallycomplexboundaryofabiologicalobjectsuchasanorganorboneintoasmallsetofshapepara-metersfacilitatesavarietyofstatisticalanalyses,includingthecharacterizationofshapevariabilityacrossanensemble;comparisonofobjectshapebetweengroups;andthetrackingofshapechangeovertime.Itisimportanttopresenttheresultsoftheseanalysesinanintuitivewaytoencouragetheconnectionoftheshapeanalysistodomain-speci cphysicalorbiologicalprocesses.Forin-stance,theinterpretabilityofstatisticaltestsofbrainregionshapedi erencesbetweenhealthyanddiseasedsubjectswouldbeenhancedifdi erencescouldN.KarssemeijerandB.Lelieveldt(Eds.):IPMI2007,LNCS4584,pp.519–531,2007.cSpringer-VerlagBerlinHeidelberg2007